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From rrosebru@mta.ca Tue May 1 12:12:36 2007 -0300
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Date: Tue, 1 May 2007 08:53:18 -0400 (EDT)
From: Michael Barr <barr@math.mcgill.ca>
To: Categories list <categories@mta.ca>
Subject: categories: Tensor products (and C*-algebras)
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I think it important to note that tensor products have no universal
mapping property and no categorical definition. Given an internal hom,
there might or might not be a tensor product that provides a left adjoint
for it. Given a bifunctor, there might or might not be an internal hom
(or two if the bifunctor is not symmetric) right adjoint to it.
Another point is that the tensor product on abelian groups (or modules
over any commutative right) has two universal mapping properties: It
provides left adjoints for the quite obvious (but still not categorically
defined) internal hom and also represents the functor that takes A to the
functor of bilinear maps out of A x B.
In any case, it makes no sense to ask what is the "right" tensor product.
The right tensor product will be the one that is appropriate to the job
you want to do with it.
Michael
From rrosebru@mta.ca Tue May 1 13:44:02 2007 -0300
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Date: Tue, 1 May 2007 16:34:26 +0100
From: Miles Gould <miles@assyrian.org.uk>
To: categories@mta.ca
Subject: categories: Re: C*-algebras
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On Sat, Apr 28, 2007 at 10:27:58PM +0200, Bas Spitters wrote:
> It seems hard to find references to a categorical treatment of
> C*-algebras. Concretely, there are several tensor products on
> C*-algebras. Which one is `the right one' from a categorical perspective?
Jeff Egger gave a talk on some of these ideas at the Nice PSSL - I'm
somewhat surprised he hasn't replied to this thread. IIRC, the category
of operator algebras is an involutive monoidal category with respect to
one or other of the tensor products, and C*-algebras are exactly the
involutive monoids w.r.t. this tensor product. Can't remember which one
it was, though.
Miles
From rrosebru@mta.ca Wed May 2 10:09:01 2007 -0300
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From: Marco Grandis <grandis@dima.unige.it>
Subject: categories: Preprint available: Collared cospans, cohomotopy and TQFT
Date: Wed, 2 May 2007 11:47:48 +0200
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The following preprint is available:
M. Grandis, Collared cospans, cohomotopy and TQFT (Cospans in
Algebraic Topology, II)
Dip. Mat. Univ. Genova, Preprint 555 (2007).
http://www.dima.unige.it/~grandis/wCub2.pdf
http://www.dima.unige.it/~grandis/wCub2.ps
Abstract. Topological cospans and their concatenation, by pushout,
appear in the theories of tangles, ribbons, cobordism, etc. Various
algebraic invariants have been introduced for their study, which it
would be interesting to link with the standard tools of Algebraic
Topology, (co)homotopy and (co)homology functors.
Here we introduce collared cospans between topological spaces, as a
generalisation of the cospans which appear in the previous theories.
Their interest lies in the fact that their concatenation is realised
with homotopy pushouts. Therefore, cohomotopy functors induce
'functors' from collared cospans to spans of sets, providing - by
linearisation - topological quantum field theories (TQFT) on
manifolds and their cobordisms. Similarly, (co)homology and homotopy
functors take collared cospans to relations of abelian groups or (co)
spans of groups, yielding other 'algebraic' invariants.
This is the second paper in a series devoted to the study of cospans
in Algebraic Topology. It is practically independent from the first,
which deals with higher cubical cospans in abstract categories. The
third article will proceed from both, studying cubical topological
cospans and their collared version.
____________
Marco Grandis
From rrosebru@mta.ca Wed May 2 14:20:37 2007 -0300
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Date: Wed, 2 May 2007 13:03:55 -0400 (EDT)
From: Jeff Egger <jeffegger@yahoo.ca>
Subject: categories: Re: C*-algebras
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--- Miles Gould <miles@assyrian.org.uk> wrote:
> Jeff Egger gave a talk on some of these ideas at the Nice PSSL - I'm
> somewhat surprised he hasn't replied to this thread.
I'm usually too shy to post to the mailing list, so I wrote Bas Spitters
a personal reply instead. In this case, though, I have to set the
record straight...
> IIRC, the category
> of operator algebras is an involutive monoidal category with respect to
> one or other of the tensor products, and C*-algebras are exactly the
> involutive monoids w.r.t. this tensor product. Can't remember which one
> it was, though.
The category of operator _spaces_ admits a (non-trivial) involutive monoidal
structure---by which I mean a (non-commutative) monoidal structure together
with a _covariant_ involution that reverses the order of tensoring.
[Regarding a monoidal category as a one-object bicategory B, this means
that the involution relates B with B^{op} rather than with B^{co}.]
The tensor product is called the _Haagerup_ tensor product, and the
involution I considered is the so-called _opposite_ operator space
structure applied to the conjugate vector space. I had conjectured that
involutive monoids in this involutive monoidal category (which, for the
purposes of this mail, I shall call involutive operator algebras) are
the same as C*-algebras, but eventually I discovered a counter-example
which showed that involutive operator algebras are strictly more general
than C*-algebras. (This was the direction which had less concerned me!)
I apologise to anyone to whom I failed to mention this counter-example.
Cheers,
Jeff.
Ask a question on any topic and get answers from real people. Go to Yahoo! Answers and share what you know at http://ca.answers.yahoo.com
From rrosebru@mta.ca Wed May 2 14:20:37 2007 -0300
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Date: Wed, 2 May 2007 10:09:42 -0700
From: Ashish Tiwari <tiwari@csl.sri.com>
To: tiwari@csl.sri.com
Subject: categories: ADDCT'07: LAST CFP: Abstract Submission Deadline May 4
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LAST CALL FOR PAPERS
Automated Deduction: Decidability, Complexity, Tractability
(ADDCT'07)
Workshop affiliated with CADE-21 Bremen,
Germany, 15 July, 2007
For complete information- http://www.mpi-inf.mpg.de/~sofronie/addct07.html
Important Dates
---------------
4 May 2007: Abstract submission
9 May 2007: Paper submission
5 June 2007: Notification
15 July 2007: Workshop
Topics of interest for ADDCT include (but are not restricted to):
-----------------------------------------------------------------
- Decidability:
- decision procedures based on logical calculi such as:
resolution, rewriting, tableaux, sequent calculi, or natural deduction
- decidability in combinations of logical theories
- Complexity:
- complexity analysis for fragments of first- (or higher) order logic
- complexity analysis for combinations of logical theories
(including parameterized complexity results)
- Tractability (in logic, automated reasoning, algebra, ...)
- Application domains for which complexity issues are essential
(verification, security, databases, ontologies, ...)
Submissions are encouraged in one of the following categories:
--------------------------------------------------------------
- Original research papers (up to 15 pages, LNCS style, including bibliogra=
phy);
- Work in progress (up to 6 pages, LNCS style, without bibliography).
- Presentation-only papers
Submission of papers is via EasyChair at http://www.easychair.org/ADDCT2007=
/
Organizers and Chairs
---------------------
Silvio Ghilardi (U. Milano)
Ulrike Sattler (U. Manchester)
Viorica Sofronie-Stokkermans (MPI,Saarbr=FCcken)
Ashish Tiwari (Menlo Park)
Program Committee
-----------------
Matthias Baaz (T.U.Wien)
Maria Paola Bonacina (U. Verona)
Christian Ferm=FCller (T.U.Wien)
Silvio Ghilardi (U. Milano)
Reiner Haehnle (Chalmers U.)
Felix Klaedtke (ETH Zurich)
Sava Krstic (Intel Corporation)
Viktor Kuncak (EPFL Lausanne)
Carsten Lutz (TU Dresden)
Christopher Lynch,(Clarkson U.)
Silvio Ranise (LORIA/INRIA-Lorraine)
Ulrike Sattler (U. Manchester)
Renate Schmidt (U. Manchester)
Viorica Sofronie-Stokkermans (MPI,Saarbr=FCcken)
Ashish Tiwari (SRI)
Luca Vigano (U. Verona)
Contact
For further informations please send an e-mail to
Viorica Sofronie-Stokkermans sofronie@mpi-inf.mpg.de
From rrosebru@mta.ca Fri May 4 15:30:29 2007 -0300
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Date: Wed, 2 May 2007 10:55:07 -0700
From: John Baez <baez@math.ucr.edu>
To: categories <categories@mta.ca>
Subject: categories: Beck-Chevalley for presheaves on groupoids?
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Hi -
One of you must know the answer to this!
Suppose we have a weak pullback (= pseudo-pullback) square of
groupoids:
G -> H
| |
v v
K -> L
Suppose we take presheaves on all four. We can get a square
hom(G^{op},Set) -> hom(H^{op},Set)
^ ^
| |
hom(K^{op},Set) -> hom(L^{op},Set)
where the arrows pointing forward - in the same direction as
the original arrows - are defined using pushforward, and the arrows
pointing backward are defined using pullback.
Does this square commute up to natural isomorphism? Do you
know a reference somewhere?
Some side remarks:
1) This seems related to the "Beck-Chevalley condition".
2) It may work for categories as well as groupoids, but I happen to
need it only for groupoids.
3) I really need it with the category Vect replacing Set, so
if you know a general result for any sufficiently nice category
playing the role of Set here, that would be wonderful.
Best,
jb
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Date: Thu, 3 May 2007 13:13:27 -0400 (EDT)
From: Michael Makkai <makkai@math.mcgill.ca>
To: Categories List <categories@mta.ca>
Subject: categories: 3rd announcement of (same) paper
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The paper "Computads and 2 dimensional pasting diagrams" has been
re-posted on my website http://www.math.mcgill.ca/makkai/. The paper is in
a single pdf.
It incorporates fresh corrections with respect to the second announcement
on April 26th.
With greetings: Michael Makkai
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for categories-list@mta.ca; Fri, 04 May 2007 15:21:45 -0300
Message-ID: <06ef01c78d6e$cd5a88d0$4601a8c0@RONNIENEW>
From: "Ronnie Brown" <ronnie.profbrown@btinternet.com>
To: <categories@mta.ca>
References: <E1Hg982-0003eY-FB@mailserv.mta.ca>
Subject: categories: multiple compositions
Date: Thu, 3 May 2007 11:35:42 +0100
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Dear Michael,
This email is suggested by your announcement at (
http://www.math.mcgill.ca/makkai/) of papers on pasting and computads.
First, I hope it is useful to direct people to an early paper with a
definition of strict omega-categories, there called \infty-categories:
(with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids
and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981)
371-386.
www.bangor.ac.uk/r.brown/pdffiles/x-comp.pdf
The main emphasis of this paper is the equivalence in the title. Because
crossed complexes C have a classifying space BC which can also be
represented as a fibration over B\pi_1 C with fibre a topological abelian
group (in fact the classifying space of a chain complex) this implies that
the homotopy type of spaces represented by \infty-groupoids is limited. This
observation suggested to Grothendieck in 1982 the need to move to weak
\infty-categories (or groupoids) for dealing with matters of nonabelian
cohomology, which for him was a long standing aim. It was not till I met him
in 1986 that I convinced him that strict n-fold groupoids really did model
all weak homotopy n-types, (Loday), at which he exclaimed `That is
absolutely beautiful!' There is still work to do on the connections with
nonabelian cohomology! And crossed complexes, though limited, are certainly
useful for this, because of their close relation to chain complexes with
operators. (for a survey on crossed complexes, see math.AT/0212274).
Second, I would like to raise some general questions on multiple
compositions and what is or should be the mathematics to deal with these.
For 2-categories, this seems to be pasting schemes. However the thrust of my
work since the 1970s has been to Higher Homotopy van Kampen theorems,
(HHvKTs) based on the question of the possible use of groupoids in higher
homotopy theory, given their success in 1-dimensional homotopy theory. The
key aim was to use cubical methods, because these gave a convenient
`algebraic inverse to subdivision', through the use of multiple
compositions, modelling steps in the proof of the usual vKT for groupoids.
Such HHvKTs were proved with Philip Higgins in dimension 2 in 1978, in all
dimensions (for crossed complexes) in 1981, and with Jean-Louis Loday in
1987 (for cat^n groups and so crossed n-cubes of group). All these theorems
have algebraic implications for homotopy types which seem unobtainable by
other means. The theorems with PJH use directly `algebraic inverse to
subdivision', while the proof with Loday uses some sophisticated algebraic
topology and simplicial methods (Waldhausen, Zisman, Puppe and some new
results). The work obtains to a limited extent a vision of Grothendieck of
what he termed `integration of homotopy types'; there are strong
connectivity assumptions so the theorems do not allow calculation of
everything, e.g. homotopy groups of spheres, and so some have said `the
theory has not fullfilled its promise' (report on a failed research
proposal). On the other hand, the theory does come within the scope of
`higher dimensional nonabelian methods for local-to-global problems', and
the new explicit calculations enabled and relations with combinatorial group
theory (e.g. the nonabelian tensor product of groups, bibiliography now of
90 items, http://www.bangor.ac.uk/~mas010/nonabtens.html) are pointers to
its success.
Possibly relevant to this is that I have never been able to write down a
proof of even the 2-dimensional HHvKT using 2-groupoids; and it would not
have been, or at least was not, even conjectured in those terms.
My preference is for algebraic models of homotopy types which lead to some
explicit algebraic computations (hence the HHvKTs), to new theorems, and
new relations with other areas.
My overall questions are therefore:
(i) to what extent can and should cubical methods be used in weak category
theory?
(ii) is there some operadic or other method from current ideas on higher
category theory which allows the use of `algebraic inverses to subdivision'
in all dimensions?
(iii) to what extent are these operadic methods generally useful in higher
dimensional nonabelian methods for local-to-global problems? (I first heard
of the term local-to-global problems from Dick Swan, when we worked on his
lecture notes on the Theory of Sheaves, Oxford, 1958.)
Of course subdivision allows the passage from global to local. The problem
is the converse, a key problem in maths and science (even biology and
engineering!). Anything which helps in this seems to me a Good Thing!
Greetings and Good Luck,
Ronnie Brown
From rrosebru@mta.ca Fri May 4 21:51:02 2007 -0300
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for categories-list@mta.ca; Fri, 04 May 2007 21:47:01 -0300
Date: Fri, 4 May 2007 15:50:31 -0400 (EDT)
From: Deniz Kural <kural@fas.harvard.edu>
To: categories@mta.ca
Subject: categories: Literature on Category Theory and Biology
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Hi,
I was wondering if you are aware of any bibliographies, reviews, or papers
relating category theory to biology - mathematical biology, systems
biology, computational biology or bioinformatics.
I would be interested in papers relating category theory to areas of
knowledge representation or other areas of computer science used in
abovementioned areas.
Please feel free to email me in person if you wish not to overburden the
mailing list.
Regards,
Deniz Kural
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for categories-list@mta.ca; Fri, 04 May 2007 21:48:14 -0300
Subject: categories: Re: Beck-Chevalley for presheaves on groupoids?
To: categories@mta.ca
Date: Fri, 4 May 2007 17:07:22 -0300 (ADT)
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From: rjwood@mathstat.dal.ca (RJ Wood)
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If
G -> H
| <= |
v v
K -> L
is a square (with a 2-cell as shown) in cat then
applying ^ =((-)^{op},Set) gives
G^<- H^
^ => ^
| |
K^<- L^
and taking the mate with respect to the horizontal adjunctions
given by left Kan extension gives
G^-> H^
^ => ^
| |
K^-> L^
If the original square is a comma square then the 2-cell in
the third square is invertible. There are squares other than
comma squares, cocomma squares for example, for which the
2-cell in the third square is invertible. See Rene Guitart's
early work on exact squares.
Best, Rj Wood
> One of you must know the answer to this!
>
> Suppose we have a weak pullback (= pseudo-pullback) square of
> groupoids:
>
> G -> H
> | |
> v v
> K -> L
>
> Suppose we take presheaves on all four. We can get a square
>
> hom(G^{op},Set) -> hom(H^{op},Set)
> ^ ^
> | |
> hom(K^{op},Set) -> hom(L^{op},Set)
>
> where the arrows pointing forward - in the same direction as
> the original arrows - are defined using pushforward, and the arrows
> pointing backward are defined using pullback.
>
> Does this square commute up to natural isomorphism? Do you
> know a reference somewhere?
>
> Some side remarks:
>
> 1) This seems related to the "Beck-Chevalley condition".
>
> 2) It may work for categories as well as groupoids, but I happen to
> need it only for groupoids.
>
> 3) I really need it with the category Vect replacing Set, so
> if you know a general result for any sufficiently nice category
> playing the role of Set here, that would be wonderful.
>
> Best,
> jb
From rrosebru@mta.ca Sat May 5 11:46:27 2007 -0300
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for categories-list@mta.ca; Sat, 05 May 2007 11:45:02 -0300
Date: Sat, 05 May 2007 10:19:49 +0300
From: Zippie Arzi-Gonczarowski <zippie@actcom.co.il>
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Subject: categories: Re: Literature on Category Theory and Biology
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Hi,
1.You may want to look at the writings of Robert Rosen (a Google search
will provide the necessary links).
2. For a different direction, and on a far more modest note, you may try
looking at some of my papers on my web page:
http://www.actcom.co.il/typographics/zippie
Of course I will be very intrested to hear your comments about that.
Good luck,
Zippie
--
____________________________________________
Zippora Arzi-Gonczarowski, Ph.D. Aka:Zippie
Typographics, Ltd.
46 Hehalutz St.
Jerusalem 96222, ISRAEL
zippie@actcom.co.il
http://www.actcom.co.il/typographics/zippie
Tel: +972-2-6437819 Fax: +972-2-6434252
_____________________________________________
From rrosebru@mta.ca Sat May 5 11:46:27 2007 -0300
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for categories-list@mta.ca; Sat, 05 May 2007 11:43:54 -0300
From: Colin McLarty <colin.mclarty@case.edu>
To: categories@mta.ca
Date: Fri, 04 May 2007 22:51:39 -0400
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Subject: categories: Re: Literature on Category Theory and Biology
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The first time the term "category theory" (I mean, exactly that term)
appeared in Mathemtical Reviews was in the review of
Rosen, R. [1961]: `A relational theory of the structural changes
induced in biological systems by alterations in environment', {\em
Bulletin of Mathematical Biophysics} \bf 23}, pp.~165--71.
The full review reads:
The author uses, among other things, some previous results from his
biologico-mathematical applications of abstract category theory [#B416]
in order to further develop another paper concerning relational biology
[#B418]. Some biological applications are treated; e.g., an
interpretation of the mitotic cycle.
Rosen's earlier related works are reviewed as dealing with "the theory
of categories."
best, Colin
----- Original Message -----
From: Deniz Kural <kural@fas.harvard.edu>
Date: Friday, May 4, 2007 8:55 pm
Subject: categories: Literature on Category Theory and Biology
To: categories@mta.ca
>
>
> Hi,
>
> I was wondering if you are aware of any bibliographies, reviews,
> or papers
> relating category theory to biology - mathematical biology, systems
> biology, computational biology or bioinformatics.
>
> I would be interested in papers relating category theory to areas of
> knowledge representation or other areas of computer science used in
> abovementioned areas.
>
> Please feel free to email me in person if you wish not to
> overburden the
> mailing list.
>
> Regards,
> Deniz Kural
>
>
>
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for categories-list@mta.ca; Sat, 05 May 2007 11:41:48 -0300
Date: Fri, 4 May 2007 13:37:32 +0200
From: Ralf Treinen <treinen@lsv.ens-cachan.fr>
To: categories@mta.ca
Subject: categories: RDP'07 First Call for Participation
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RDP 2007 - Call for Participation
Federated Conference on Rewriting, Deduction, and Programming
June 25 to 29, Paris, France
http://www.rdp07.org
========================================================================
Online Registration is open unil May, 31.
========================================================================
RDP'07 is the fourth edition of the International Conference on Rewriting,
Deduction, and Programming, consisting of two main conferences
* Rewriting Techniques and Applications (RTA'07)
* Typed Lambda Calculi and Applications (TLCA'07)
a colloquium
* From Type Theory to Morphologic Complexity: a Colloquium in Honor of
Giuseppe Longo
as well as the following workshops:
* Higher Order Rewriting (HOR)
* Proof Assistants and Types in Education (PATE)
* Rule-Based Programming (RULE)
* Security and Rewriting Techniques (SecReT)
* Unification (UNIF)
* Functional and (Constraint) Logic Programmming (WFLP)
* Reduction Strategies in Rewriting and Programming (WRS)
* Termination (WST)
Invited Speakers:
=================
Joint RTA/TLCA: * Frank Pfenning (Carnegie Mellon University)
TLCA: * Patrick Baillot (CNRS, University Paris 13)
* Greg Morrisett (Harvard University)
RTA: * Xavier Leroy (INRIA Rocquencourt)
* Robert Nieuwenhuis (Technical University of Catalonia)
Celebratation of the 75th anniversary of the lambda calculus:
* Henk Barendregt (Nijmegen University)
Registration:
=============
http://www.rdp07.org/registration.html
Student Travel Grants:
======================
A limited number of travel grants for students is available. A call
for applications will be issued separately. Information about travel
grants will also be published on http://www.rdp07.org/grants.
From rrosebru@mta.ca Sat May 5 21:20:13 2007 -0300
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for categories-list@mta.ca; Sat, 05 May 2007 21:08:53 -0300
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Subject: categories: Re: Literature on Category Theory and Biology
Date: Sat, 5 May 2007 11:44:43 -0400
From: "Wojtowicz, Ralph" <wojtowicz@metsci.com>
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The links:
http://perso.orange.fr/vbm-ehr/
and=20
http://alf.nbi.dk/%7Eemmeche/coPubl/97d.NABCE/ExplEmer.html =20
and a related paper "Categorical language and hierarchical models for
cell systems" by R. Brown, R. Paton and T. Porter may be of interest. I
believe that Brown and Porter have other references of this nature. See
also the recent work by M. Healy on neural networks.
Best wishes,
Ralph Wojtowicz
wojtowicz@metsci.com
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for categories-list@mta.ca; Sat, 05 May 2007 21:09:59 -0300
Date: Sat, 05 May 2007 18:42:30 +0200
From: Andree Ehresmann <andree.ehresmann@u-picardie.fr>
To: categories@mta.ca
Subject: categories: Re: Literature on Category Theory and Biology
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In answer to Deniz Kural
With Jean-Paul Vanbremeersch we have been developing a model for
biological and neural systems based on category theory called Memory
Evolutive Systems. Since 20 years we have published a series of papers
on this subject, most of which are posted on our Internet site
http://perso.wanadoo.fr/vbm-ehr
Recently we have written a book on this subject:
Memory Evolutive sytems: hierarchy, emergence, cognition"
due to appear this month in the series "Studies in
Multidisciplinarity" of Elsevier (volume 4).
Sincerely
Andree C. Ehresmann
From rrosebru@mta.ca Sat May 5 21:26:31 2007 -0300
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for categories-list@mta.ca; Sat, 05 May 2007 21:24:54 -0300
From: "David Ellerman" <david@ellerman.org>
To: <cat-dist@mta.ca>
Subject: categories: Re: Literature on Category Theory and Biology
Date: Sat, 5 May 2007 09:01:45 -0700
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A new "heteromorphic" treatment of adjoint functors provides applications to
biology such as an abstract characterization of selectionist (as opposed to
instructionist) mechanisms as in Darwin's evolutionary theory, the
selectionist theory of the immune system, and neural darwinism (e.g.,
Edelman's and Changeux's work). Heteromorphisms, e.g., the injection of a
set of generators into the free group on the set, can be formally treated in
category theory using bifunctors Het:X^op x A--> Set analogous to the usual
Hom:X^op x X-->Set. When the heteromorphisms from objects in a category X to
objects in a category A can represented in each of the categories, then the
functors giving the representing objects are a pair of adjoint functors and
the representations give a pair of natural isomorphisms:
Hom_A(Fx,a) = Het(x,a) = Hom-_X(x,Ga).
The usual treatment of adjoints leaves out the middle term. And all adjoint
functors can be shown to arise in this manner (up to isomorphism). The
applications were not available in the usual treatment of adjoints where the
heteromorphisms were not explicit.
The applications are outlined in a paper just published in Axiomathes (2007)
17: 19-39. A reprint can be retreived from my website:
http://www.ellerman.org/Davids-Stuff/Maths/Adjoints-Axiomathes-Reprint.pdf .
A rather long (and impenetrable) treatment of the math was in the recent
"What is Category Theory" collection of papers (2006: Polimetrica). A short
straightforward treatment of the math is available on the ArXiv:
http://arxiv.org/abs/0704.2207v1 .
Other applications of category theory to biology have been made by Robert
Rosen (as mentioned by several posts) and by Andree Ehresmann.
Best, David
__________________
David Ellerman
Visiting Scholar
University of California at Riverside
Email: david@ellerman.org
Webpage: www.ellerman.org
View my research on my SSRN Author page:
<http://ssrn.com/author=294049> http://ssrn.com/author=294049
From rrosebru@mta.ca Mon May 7 10:07:59 2007 -0300
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From: Francois Lamarche <lamarche@loria.fr>
Subject: categories: PSSL 86 in Nancy: Preliminary Announcement
Date: Mon, 7 May 2007 13:16:00 +0200
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Fellow category theorists,
The 86th edition of the Peripatetic Seminar on Sheaves and Logic will =20=
be held at the Institut =C9lie Cartan of the Universit=E9 Henri Poincar=E9=
=20
in Nancy, on the weekend of September 8-9 2007.
More details will be announced later this summer, but interested =20
people can start contacting me now. We intend to continue the PSSL =20
tradition of informality, and scheduling talks pertaining to any =20
aspect of category theory, with or without applications in natural =20
science, logic, computer science, or other branches of mathematics.
The fast TGV-Est train line will be inaugurated in June, and the =20
Paris-Nancy trip will then take only 1h30m, with easy connections to =20
the two Paris airports. The city of Nancy is right on the Paris-=20
Munich train line, and also has good train connecftions with the =20
north (Luxembourg, Brussels and Frankfurt via Metz) and the south =20
(Lyon, Nice...). There is a local airport, 45 minutes away from =20
downtown by minibus shuttle, and there are also two relatively close =20
international airports, Luxembourg and Strasbourg, which often allow =20
you to do the airport-dowtown Nancy trip in less than 2h30m.
Nancy is of considerable interest for the mathematical tourist, being =20=
the birthplace of Henri Poincar=E9, and being intimately related to the =20=
career of Nicolas Bourbaki. It has two historical old towns: the =20
medieval one, with the Renaissance palace of the Dukes of Lorraine, =20
and the classical one, with UNESCO World heritage sites built by Duke =20=
Stanislas. It is can also boast one of the highest concentrations of =20
Art Nouveau architecture in all of Europe, rivalling Prague and =20
Barcelona.
Hoping to see you in September,
Fran=E7ois Lamarche
http://www.loria.fr/~lamarche
From rrosebru@mta.ca Mon May 7 19:47:28 2007 -0300
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for categories-list@mta.ca; Mon, 07 May 2007 19:42:25 -0300
Date: Mon, 7 May 2007 13:03:27 -0600 (MDT)
Subject: categories: Re: Literature on Category Theory and Biology
From: mjhealy@ece.unm.edu
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Regarding Deniz Kural's question about references to papers on category
theory and biology, Tom Caudell and I have been investigating a semantic
theory for neural networks both biological and artificial, cognitive and
non-cognitive. We are designing and conducting experiments to test and
refine the theory in both neuroscience and cognitive psychology working
with colleagues in those disciplines. An initial paper on the theory is
M. J. Healy and T. P. Caudell (2006)
Ontologies and Worlds in Category Theory: Implications for Neural Systems=
,
Axiomathes, vol. 16, nos. 1-2, pp. 165-214.
The only experiment appearing in a publication to date is one on an
artificial neural network application, presented at IJCNN 2005 in Montrea=
l
(the results were presented also at CT06).
Regards,
Mike Healy
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for categories-list@mta.ca; Wed, 09 May 2007 09:12:16 -0300
Date: Wed, 9 May 2007 08:17:38 GMT
From: Jeremy.Gibbons@comlab.ox.ac.uk
To: categories@mta.ca
Subject: categories: Integrated Formal Methods 2007: Call for participation
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IFM2007: INTEGRATED FORMAL METHODS
CALL FOR PARTICIPATION
2nd to 5th July 2007
St Anne's College, Oxford, UK
www.ifm2007.org
The design and analysis of computing systems presents a significant
challenge: systems need to be understood at many different levels of
abstraction, and examined from many different perspectives. Formal
methods - languages, tools, and techniques with a sound, mathematical
basis - can be used to develop a thorough understanding, and to support
rigorous examination.
Further research into effective integration is required if these
methods are to have a significant impact outside academia. The IFM
series of conferences seeks to promote that research, to bring
together the researchers carrying it out, and to disseminate the
results of that research among the wider academic and industrial
community.
This is the sixth IFM conference. It will be held in the historic
university town of Oxford, at St Anne's College - one of the larger
colleges of the University, with excellent new conference
facilities. Oxford is easily reached from most UK cities, and is 70
minutes from the country's largest airport. Earlier conferences in
the series were held at York (1999), Schloss Dagstuhl (2000), Turku
(2002), Kent (2004), and Eindhoven (2005).
The conference runs for three full days, 3rd to 5th July. Invited
speakers include Jifeng He on "UTP Semantics for Web Services" and
Daniel Jackson on "Recent Advances in Alloy"; a third invited speaker
is yet to be confirmed. There are 32 contributed papers, including a
special session on Unifying Theories of Programming. In addition,
there are four satellite events, taking place on 2nd and 3rd July -
three workshops:
* Refinement Workshop
* C/C++ Verification
* MeMoT (Methods, Models and Tools for Fault Tolerance)
and a tutorial:
* KeY (Integrating OO Design and Deductive Verification of Software)
The full programme is available at:
http://www.ifm2007.org/programme-ifm.html
Registration for the conference is now open, at:
http://www.ifm2007.org/registration.html
Special early-registration fees apply until 1st June 2007.
For more information, visit the conference web page:
http://www.ifm2007.org/
or contact the local organisers:
Jim Davies http://www.softeng.ox.ac.uk/Jim.Davies
Jeremy Gibbons http://www.softeng.ox.ac.uk/Jeremy.Gibbons
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for categories-list@mta.ca; Wed, 09 May 2007 09:18:49 -0300
From: Marco Grandis <grandis@dima.unige.it>
Subject: categories: The policy of arXiv
Date: Wed, 9 May 2007 11:40:48 +0200
To: LIBGATEWAY-L@cornell.edu, categories@mta.ca
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Dear Sirs,
Before deciding of using arXiv in a systematic way, I would like that =20=
there be a clear statement of its policy and commitments; a statement =20=
which, likely, the organisers and many of us take as understood and =20
granted, but which I have been unable to find.
To be more explicit, what about the possibility of the system being, =20
in future, exploited economically? What about the possibility of it =20
being sold to a commercial company?
When downloading an article to the arXiv, the author is asked to =20
grant 'a perpetual, non-exclusive license to distribute this =20
article'. I think the author has a right to know that this license =20
will not be used, in the future, for goals which would be in contrast =20=
with the present (understood) ones, or even opposite to them.
Last year I wrote a message in this sense to the list =20
'categories' (categories@mta,ca), where arXiv has been frequently =20
proposed as a way of disseminating articles. In December 2006 there =20
was a discussion about these points in a blog kept by John Baez
http://golem.ph.utexas.edu/category/2006/12/=20
arxiv_policy_statement.html
This is part of a posting by John Baez, on this blog:
"Many people like to have some idea of what an organization seeks to =20
do, or is committed to do, before they do business with it.
For this reason, it=92s unusual for such an important entity as the =20
arXiv not to make a public statement about its goals and commitments. =20=
Consider, for example, the Berlin Declaration on Open Access to =20
Knowledge in the Sciences and Humanities, and its many signatories, =20
or the statement by the Wellcome Trust supporting open access, or the =20=
Wikimedia mission statement and bylaws, or the Google code of conduct =20=
and privacy policy. " (end of citation)
As far as I know, there still is no policy statement available. One =20
can only read, at the head of the 'arXiv Advisory Board' page:
"Please note that all arXiv policy decisions are ultimately made by =20
Cornell University Library."
Will the Cornell University Library make its arXiv policy public?
With best regards
Marco Grandis
Dipartimento di Matematica
Universit=E0 di Genova
Via Dodecaneso, 35
16146 Genova
Italy
e-mail: grandis@dima.unige.it
tel: +39 010 353 6805
http://www.dima.unige.it/~grandis/=
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for categories-list@mta.ca; Thu, 10 May 2007 08:34:21 -0300
Date: Wed, 9 May 2007 07:35:28 -0700 (PDT)
From: Bill Rowan <rowan@transbay.net>
To: categories@mta.ca
Subject: categories: Re: The policy of arXiv
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Hi all,
I think it is relevant to point out that if people who post articles to
the Arxiv agree to grant a permanent, _non-exclusive_ right to distribute the
article, that means, that if the operators of the Arxiv, whoever
they are, decide to sell copies of the database, or individual articles,
they won't be entitled to prevent anyone else from distributing the
same material for free. So they can't corner the market on the content,
in other words.
All in all it doesn't seem that big of a concern to me, although certainly
worth a thoughtful discussion. It would be nice to hear from Cornell
Library about their intentions.
Bill Rowan
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for categories-list@mta.ca; Fri, 11 May 2007 20:19:57 -0300
From: "Philip Mulry" <pmulry@mail.colgate.edu>
To: categories@mta.ca
Subject: categories: FMCS 2007 - Final Call for Participation
Date: Fri, 11 May 2007 13:59:55 -0400
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****************************************************
Final Announcement - FMCS 2007
This is the final call for participation in FMCS 2007
*** The registration deadline is May 20.
*** University accommodations can not be guaranteed after that date.
The Department of Computer Science at Colgate University is hosting
Foundational Methods in Computer Science 2007 on the Colgate University
campus in Hamilton N.Y.
Dates: Arrival on Thursday June 7, 2007 (Reception in the evening).
Scientific Program Friday June 8 - Sunday June 10 (ends mid-day).
The workshop is an annual meeting meant to bring together researchers in
mathematics and computer science with a focus on the application of category
theory in computer science. The meeting will begin with a day of research
tutorials, followed by a day and a half of research talks.
Invited speakers this year include:
a.. Steve Awodey(Carnegie Mellon)
b.. Steve Bloom(Stevens)
c.. Robin Cockett (Calgary)
d.. Paul Hudak(Yale)
e.. Ernie Manes (U Mass)
f.. Robert Rosebrugh(Mount Allison)
The remaining research talks are solicited from participants.
Time slots are limited, so please register early if you would like to be
considered for a talk.
Graduate student participation is particularly encouraged at FMCS 2007.
Students will pay a reduced registration fee.
Conference Link: http://cs.colgate.edu/faculty/mulry/FMCS2007/FMCS2007.html
Contacts
The local organizer of FMCS 2007 is: Philip Mulry
The secretary for FMCS 2007 is Char Jablonski
From rrosebru@mta.ca Sat May 12 19:50:22 2007 -0300
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for categories-list@mta.ca; Sat, 12 May 2007 19:43:08 -0300
Date: Sat, 12 May 2007 10:51:10 -0300 (BRT)
Subject: categories: WoLLIC'2007 - Call for Participation
From: ruy@cin.ufpe.br
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[** sincere apologies for duplicates **]
Call for Participation
14th Workshop on Logic, Language, Information and Computation
(WoLLIC'2007)
Rio de Janeiro, Brazil
July 2-5, 2007
(a satellite event to Brazilian Computer Society Conference - CSBC'07)
WoLLIC is an annual international forum on inter-disciplinary research
involving formal logic, computing and programming theory, and natural
language and reasoning. Each meeting includes invited talks and
tutorials as well as contributed papers.
The Fourteenth WoLLIC will be held in Rio de Janeiro, Brazil, from
July 2 to July 5, 2007, in conjunction with the 27th Brazilian
Computer Society Conference. It is sponsored by the Association for
Symbolic Logic (ASL), the Interest Group in Pure and Applied Logics
(IGPL), the European Association for Logic, Language and Information
(FoLLI), the European Association for Theoretical Computer Science
(EATCS), the Sociedade Brasileira de Computacao (SBC), and the
Sociedade Brasileira de Logica (SBL).
PROCEEDINGS
The proceedings of WoLLIC'2007, including both invited and contributed
papers, will be published in advance of the meeting as a volume in
Springer's Lecture Notes in Computer Science. In addition,
abstracts will be published in the Conference Report section of
the Logic Journal of the IGPL, and selected contributions will
be published as a special post-conference WoLLIC'2007 special issue
of the journal Information and Computation.
INVITED SPEAKERS
Alex Borgida (Rutgers)
Alessandra Carbone (Paris)
Martin Escardo (Birmingham)
Philippa Gardner (Imperial Coll)
Achim Jung (Birmingham)
Louis Kauffman (U Illinois Chicago)
Michael Moortgat (Utrecht)
Paulo Oliva (London/QM)
John Reif (Duke)
Yde Venema (Amsterdam)
TUTORIAL LECTURES
Stone duality, by A. Jung
Quantum topology and quantum computation, by L. Kauffman
Biological computing, by J. Reif
INVITED TALKS
Description Logics: formal foundations and applications, by A. Borgida
Group Theory and Classical Proofs, by A. Carbone
Algorithmic Topology of Program Types, by M. Escardo
Contex Logic and Tree Update, by Ph. Gardner
On the interplay of logic and information: A topological analysis,
by A. Jung
Spin networks in quantum computation, by L. Kauffman
Symmetries in natural language syntax and semantics:
the Lambek-Grishin calculus, by M. Moortgat
Computational Interpretations of Classical Linear Logic, by P. Oliva
Autonomous programmable biomolecular devices using self-assembled DNA
nanostructures specifying properties of data DNA Nanostructures,
by J. Reif
A modal distributive law, by Y. Venema
BOOK EXHIBITION
The following publishers are expected to be exhibiting various books
from their catalogue, prospectuses, journal samples, etc., and there
will be a chance to order items at promotional prices:
The MIT Press
Springer-Verlag
A K Peters
Cambridge Univ Press
CSLI Publications (Stanford Univ)
Oxford Univ Press
World Scientific
It is likely that a few other international publishers will also take
part in the book exhibit.
PROGRAM COMMITTEE
Samson Abramsky (U Oxford)
Michael Benedikt (Bell Labs)
Lars Birkedal (ITU Copenhagen)
Andreas Blass (U Michigan)
Thierry Coquand (Chalmers U, Goteborg)
Jan van Eijck (CWI, Amsterdam)
Marcelo Finger (U Sao Paulo)
Rob Goldblatt (Victoria U, Wellington)
Yuri Gurevich (Microsoft Redmond)
Hermann Haeusler (PUC Rio)
Masami Hagiya (Tokyo U)
Joseph Halpern (Cornell U)
John Harrison (Intel UK)
Wilfrid Hodges (U London/QM)
Phokion Kolaitis (IBM Almaden Research Center)
Marta Kwiatkowska (U Birmingham)
Daniel Leivant (Indiana U) (Chair)
Maurizio Lenzerini (U Rome)
Jean-Yves Marion (LORIA Nancy)
Dale Miller (Polytechnique Paris)
John Mitchell (Stanford U)
Lawrence Moss (Indiana U)
Peter O'Hearn (U London/QM)
Prakash Panangaden (McGill, Montreal)
Christine Paulin-Mohring (Paris-Sud, Orsay)
Alexander Razborov (Steklov, Moscow)
Helmut Schwichtenberg (Munich U)
Jouko Vaananen (U Helsinki)
ORGANISING COMMITTEE
Marcelo da Silva Correa (U Fed Fluminense)
Renata P. de Freitas (U Fed Fluminense)
Ana Teresa Martins (U Fed Ceara')
Anjolina de Oliveira (U Fed Pernambuco)
Ruy de Queiroz (U Fed Pernambuco, co-chair)
Petrucio Viana (U Fed Fluminense, co-chair)
WEB PAGE
www.cin.ufpe.br/~wollic/wollic2007
---
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From: Ross Street <street@ics.mq.edu.au>
Subject: categories: An obituary for Max
Date: Mon, 14 May 2007 15:44:55 +1000
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See the latest issue of the Aust Math Soc Gazette
<http://www.austms.org.au/Gazette>
Ross
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Subject: categories: CALCO-07 - Call for Participation
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CALCO 2007
2nd Conference on Algebra and Coalgebra in Computer Science
CALCO Tools Day
August 20-24, 2007, Bergen, Norway
May 16 Early Registration deadline
July 1 Registration deadline
------------------------------------------------------------------
http://www.ii.uib.no/calco07/
------------------------------------------------------------------
August 20 CALCO-jnr, CALCO-tools
August 21-24 CALCO technical programme
CALCO'07 takes place at the Grand Hotel Terminus in Bergen, one of many
historic hotels in Norway. The conference starts Monday with two workshops
followed by an official reception Monday evening. The main program runs
Tuesday through Friday, each morning starting with an invited speaker.
Additional events are excursion by boat in the Bergen archipelago
(Wednesday afternoon) and conference dinner on one of the mountains
surrounding the city centre (Thursday afternoon).
Registration
------------
Registration fee is 3200 NOK (1200 NOK for students), with substantial
discounts for early registration. The fee includes the full conference
with all workshops, a copy of the proceedings,=20
lunches and coffee breaks, internet access and=20
the official reception Monday evening.
Registration is via the calco07 web site:
http://www.ii.uib.no/calco07/
Note that Bergen is very busy during the tourist season, so early booking
of accommodation and transportation is recommended.
Main CALCO'07 conference
------------------------
CALCO is a high-level, bi-annual conference. It brings together
researchers and practitioners to exchange new results related
to foundational aspects and both traditional and emerging uses of
algebras and coalgebras in computer science. The study of algebra
and coalgebra relates to the data, process and structural aspects of
software systems. The accepted papers report results of theoretical work
on the mathematics of algebras and coalgebras, the way these results
can support methods and techniques for software development, as well as
experience with the transition of resulting technologies into industrial
practise. Some main key words are:
* Abstract models and logics
* Specialised models and calculi
* Algebraic and coalgebraic semantics
* System specification and verification
The list of accepted papers is available at the web site.
Invited speakers
----------------
Stephen L. Bloom, Stevens Institute of Technology, NJ, USA
Prof. Bloom works on algebraic specification theories and was instrumental
in developing iterative theories, an elaborate coalgebraic method -
predating coalgebras.
Luis Caires, New University of Lisbon, Portugal
Prof. Caires has made important contributions to the field of distributed
and mobile systems, and spatial logics for these.
Barbara K=88=8Fnig, University of Duisburg-Essen, Germany
Prof. K=88=8Fnig works on graph transformation systems, with applications
to concurrent and mobile systems, software reliability and security.
Glynn Winskel, University of Cambridge, United Kingdom
Prof. Winskel is well-known for his fundamental work in semantics and
theory of concurrency.
CALCO-jnr (CALCO Young Researchers Workshop)
--------------------------------------------
CALCO-jnr is dedicated to presentations by PhD students and by those who
completed their doctoral studies within the past few years. This year
12 contributions within the theme of CALCO have been accepted. See the
overview on the CALCO-jnr web page on the CALCO web site.
--
http://www.ii.uib.no/calco07/
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Date: Fri, 18 May 2007 12:52:13 -0500 (CDT)
From: MYV <myv@cs.rice.edu>
To: vardi@cs.rice.edu
Subject: categories: Book - Finite Model Theory and Its Applications
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Finite Model Theory and Its Applications
by
Erich Graedel, Phokion G. Kolaitis, Leonid Libkin, Maarten Marx,
Joel Spencer, Moshe Y. Vardi, Yde Venema, and Scott Weinstein
Springer, 2007, 437 pages, hardcover,
ISBN: 978-3-540-00428-8.
(Series: Texts in Theoretical Computer Science. An EATCS Series)
>From the back cover: This book gives a comprehensive overview of central
topics in finite model theory - expressive power of logics, descriptive
complexity, and zero-one laws - together with selected applications
relating to database theory and artificial intelligence, especially
constraint databases and constraint satisfaction problems. The final
chapter provides a concise modern introduction to modal logic,
emphasizing the interaction with finite model theory. The underlying
theme of the book is the use of first-order, second-order, fixed-point,
and infinitary logic, as well as various fragments of and hierarchies
within these logics, to gain insight into phenomena and problems in
complexity theory and combinatorics.
The book emphasizes the use of combinatorial games, such as extensions
and refinements of the Ehrenfeucht-Fraissi games, as a powerful way to
analyze the expressive power of logics, and illustrates how sophisticated
notions from model theory and combinatorics, such as o-minimality and
treewidth, arise naturally in the applications of finite model theory
to database theory and artificial intelligence.
Students of logic and computer science will find here the tools
necessary to embark on research into finite model theory, and all
readers will experience the excitement of a vibrant area of the
applications of logic to computer science.
Table of contents:
1.Unifying Themes in Finite Model Theory
2.On the Expressive Power of Logics on Finite Models
3.Finite Model Theory and Descriptive Complexity
4.Logic and Random Structures
5.Embedded Finite Models and Constraint Databases
6.A Logical Approach to Constraint Satisfaction
7.Local Variations on a Loose Theme: Modal Logic and Decidability
To order, see http://www.springer.com/978-3-540-00428-8
From rrosebru@mta.ca Wed May 23 07:09:42 2007 -0300
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Date: Wed, 23 May 2007 08:47:43 +0100
From: Alexander Kurz <kurz@mcs.le.ac.uk>
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Subject: categories: hyperdoctrines and cylindric algebras
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There clearly is a connection between hyperdoctrines and cylindric
algebras.
Does anybody knows work that relates the two? Or that makes use of a
result from one area to prove something in the other?
I would be greatful for any reference or comment.
Best wishes,
Alexander
From rrosebru@mta.ca Thu May 24 08:04:53 2007 -0300
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Date: Thu, 24 May 2007 00:46:38 -0400
From: "Zinovy Diskin" <zdiskin@cs.toronto.edu>
Subject: categories: Re: hyperdoctrines and cylindric algebras
To: categories <categories@mta.ca>
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On 5/23/07, Alexander Kurz <kurz@mcs.le.ac.uk> wrote:
> There clearly is a connection between hyperdoctrines and cylindric
> algebras.
>
yes, of course. Roughly speaking, they are equivalent: hyperdoctrines
(HDs) are indexed category style algebraization of first order logic
while cylindric algebras (CAs) are an equivalent fibrational
formulation. To make it precise, we need to consider a few rather
straightforward yet technically bulky generalizations of both notions,
reproducing in HDs the classical context of CAs and vice versa. I'm
traveling and do not have references at hand, but below is an outline
of how it can be done (apologies for possible inaccuracies).
> Does anybody knows work that relates the two? Or that makes use of a
> result from one area to prove something in the other?
>
The last question is interesting. If we are speaking about pure
algebra, there is nothing exciting in "switching" between HDs and CAs:
these are just different representation of the same algebraic theory.
More accurately, HDs are equivalent to locally finite CAs, which are
not equationally definable. Thus, HDs are much more manageable
algebraically (but many-sorted). This trade-off between number of
sorts and equational definability is probably the most/only
interesting algebraic point.
However, the main driving force of CA development was in the
representation theorems, which are for CAs are much more intricate
than Stone representation theorems for Boolean algebras. In the
companion volume to the classical monograph by Henkin, Monk,Tarsky
(where the great trio is joined by Andreka & Nemeti), there is a lot
of interesting and not-easy-to-prove representation theorems (googling
Andreka-Nemeti should provide references). I'm not aware of any
similar results (or even interest in such results) for HDs.
ZD
== 8< == equivalence of HDs and CAs: a rough outline
Let's fix a countable set V (of variables). Consider a simple version
of the notion of hyperdoctrine, p:T-->BA^op is an indexed cat, where
T=Pow_fin(V) is the category of finite subsets of V and mappings
between them and BA is the category of Boolean algebras. Now we apply
to p the Grothendieck construction and get a fibration \delta: G-->T.
A straitforward check shows that G is a locally finite cylindric
algebra (CA). (Special axioms regulating interactions of substitutions
and bound variables hold because of Beck-Chevalle and Frobenius
conditions). Conversely, if A is a locally finite cylindric algebra
over V and a\in A, define
\delta(a) = {x \in V| C_x(a) not= a} (C_x is cylindrification
operator/quantifier). As a Boolean algebra, A is an order category
and \delta is a fibration. Its indexed version gives an HD over a
trivial algebraic theory (and with Boolean fibres).
To get an equivalence result for non-trivial algebraic theories, the
notion of CA over a variety was introduced (first by Boris Plotkin for
Halmos' polyadic algebras, and then by Janis Cirulis for CAs). To
extend equivalence for the classical HDs where fibres are
intuitionistic, we need the notion of cylindric Heyting algebras. To
extend the equivalence for CAs that are not locally finite, we need
HDs over Ts being cats with any products (not necessary finite).
Another version of equivalence results can be obtained if we replace
CAs by polyadic algebras introduced by Halmos. One more delicate point
is that CAs are equivalent to polyadic algebras with equality while
there are also polyadic algebras without equality.
Such things were popular at Riga algebraic seminar about twenty years
ago. I think that then I wrote a preprint where all this was carefully
formulated; hopefully, I still have a hard copy (never thought that
anybody would need it :).
> I would be greatful for any reference or comment.
>
> Best wishes,
>
> Alexander
>
>
>
>
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To: LICS List <lics@informatik.hu-berlin.de>
From: Kreutzer + Schweikardt <lics@informatik.hu-berlin.de>
Subject: categories: LICS 2007 - Call for Participation
Date: Wed, 23 May 2007 12:48:42 +0200 (CEST)
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LICS 2007
Call for Participation
Reminder: Early registration deadline is approaching:
May 31st, 2007
LICS 2007 will be held in the Institute of Computer Science,
University of Wroclaw, Poland, 10th - 14th July 2007.
It will be colocated with:
- International Colloquium on Automata, Languages and Programming
(ICALP 2007), 9th - 13th July 2007, and
- ASL European Summer Meeting (Logic Colloquium 2007),
14th - 19th July 2007.
The IEEE Symposium On Logic In Computer Science (LICS) is an annual
international forum on theoretical and practical topics in computer
science that relate to logic broadly construed.
Detailed information can be found on the webpage:
- http://www.informatik.hu-berlin.de/lics/lics07/
- http://july2007.ii.uni.wroc.pl/
Important dates:
- May 31st 2007: Early registration discount expires.
- 10th - 14th July 2007: Conference
Invited Speakers:
- Thomas Hales (University of Pittsburgh)
- Martin Hyland (University of Cambridge)
- Phokion Kolaitis (IBM Almaden Research Centre)
- Gordon Plotkin (University of Edinburgh)
- Michael Rabin (Harvard University and Hebrew University)
- Colin Stirling (University of Edinburgh)
From rrosebru@mta.ca Tue May 29 06:08:13 2007 -0300
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Date: Mon, 28 May 2007 16:03:49 -0400 (EDT)
From: Bill Lawvere <wlawvere@buffalo.edu>
To: categories <categories@mta.ca>
Subject: categories: Re: hyperdoctrines and cylindric algebras (Correction)
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Hyperdoctrines (in many variants) were introduced as an algebraic
aspect of "proof theory" and as such are definitely not equivalent
to cylindric algebras (or polyadic algebras or even various categorical
formulations of logic). They involve fibered categories whose fibers
are cartesian closed (and with adjoints between the fibers etc.).
The poset reflection of these fibers are Heyting algebras. This
reflection process was intuited already by Curry and was later called
"the Curry-Howard isomorphism" even though this is a serious misnomer
because it is very far from being an isomorphism.
(See my paper Adjoints in and among bi-categories, Logic & Algebra,
Lecture Notes in Pure and Applied Mathematics. 180:181-189.
Ed. A. Ursini, P Agliano, Marcel Dekker, Inc. Basel, 1996,
as well as the author's commentary on my paper Adjointness in
Foundations, as reprinted in TAC.
Recent papers of Matias Menni further clarify these developments,
which were partly inspired by work of Hans Laeuchli.)
Conceptually, the problem of presentation of a theory in algebraic
logic by means of primitive predicates and axioms can be viewed as
taking place in two steps: first the presentation of a hyperdoctrine
with non-trivial fibers, and then the further collapse by imposing
the condition that projection maps act as inverse to diagonal maps
(within each fiber). This process can be localized. The problematic
existential quantifier which is the core problem of proof theory:
("there exists a proof of ....") is thus split into several parts
to be studied separately.
I hope the above helps to clarify the relationship between two
levels of categorical algebra.
Bill
************************************************************
F. William Lawvere, Professor emeritus
Mathematics Department, State University of New York
244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
Tel. 716-645-6284
HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere
************************************************************
On Thu, 24 May 2007, Zinovy Diskin wrote:
> On 5/23/07, Alexander Kurz <kurz@mcs.le.ac.uk> wrote:
> > There clearly is a connection between hyperdoctrines and cylindric
> > algebras.
> >
>
> yes, of course. Roughly speaking, they are equivalent: hyperdoctrines
> (HDs) are indexed category style algebraization of first order logic
> while cylindric algebras (CAs) are an equivalent fibrational
> formulation. To make it precise, we need to consider a few rather
> straightforward yet technically bulky generalizations of both notions,
> reproducing in HDs the classical context of CAs and vice versa. I'm
> traveling and do not have references at hand, but below is an outline
> of how it can be done (apologies for possible inaccuracies).
>
...
From rrosebru@mta.ca Thu May 31 07:48:20 2007 -0300
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Date: Tue, 29 May 2007 10:37:00 -0400
From: "Zinovy Diskin" <zdiskin@cs.toronto.edu>
Subject: categories: Re: hyperdoctrines and cylindric algebras (Correction)
To: categories <categories@mta.ca>
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I'm afraid that still some clarification is needed. Standard
hyperdoctrines (HDs) and standard cylindric algebras (CAs) are not
equivalent by the following two groups reasons.
(1) How we model logic/predicates. In HDs, objects in fibers are
predicates of finite arities, the logic is intuitionistic and we are
interested in proofs (arrows) rather than just provability (partial
order). In CAs (of dimension \alpha = enumeration of some predefined
set of variables), elements are to be thought of as predicates of
arity \alpha, the logic is classical and we are interested in the
partial order of provability (CAs are Boolean algebras with an extra
structure).
(2) How we model algebra/terms. In an HD T-->Cat^op, the algebraic
base T is an *arbitrary* finitary algebraic theory. In CAs, the
algebraic base is *the trivial* finitary algebraic theory over \alpha,
whose only operations are projections.
The difference is quite evident , and I believe that the actual
question was not about the difference but rather about how to figure
out the commonalities (and formulate equivalence if it can be
formulated).
Result 1: adjusting HDs to CAs and PAs (polyadic algebras). The
following three notions are equivalent:
-- locally finite CA (of dimension \omega),
-- locally finite PA with equality,
-- HD, whose fibers are Boolean algebras and the algebraic base has no
morphisms other than projections.
The condition of being locally-finite can be removed if we define HDs
over algebraic bases having countable (rather than just finite)
products.
Result 2: adjusting CAs/PAs to HDs. The following three notions are equivalent:
-- HD, whose fibers are posets,
-- locally finite "polyadic Heyting algebra" with equality over a variety,
-- locally finite "cylindric Heyting algebra" over a variety.
Many similar equivalence results in-between and around the two above
can be formulated. Roughly, anything that can be defined for poset HDs
in the fibred fashion, can be reproduced for CA/PAs in the globalistic
fashion (via the Grothendieck construction) and vice versa. However,
the HD formalism is much more flexible as can be seen already from the
two results above. Result 1 is conceptually and technically easy.
Result 2 is equally easy conceptually but is much more intricate
technically. Defining polyadic Heyting algebras needs a certain
technical work, which is essentially nothing but reproducing the basic
Lawvere's observation of quantifiers as adjounts in the global Heyting
algebra setting.
In general, the notion of CA of an infinite dimension is conceptually
messy: elements are predicates of infinite arities while quantifiers
and variable substitutions are finitary (and even worse, substitutions
are not a basic notion and need to be derived via diagonals, see Janis
Cirulis' papers. But once again, the main concern of developing CAs
was to algebraize semantics -- algebras of relations, rather than
syntax and proof theory). Halmos' polyadic algebras are conceptually
more consistent in this sense (and probably because in their design
the syntactical side was taken more seriously) .
Despite all these technical differences, HDs are CAs/PAs are close in
the sense that they both follow the same basic idea of algebraizing
logic: the algebras are generated by signatures and axioms
(theories). In a bit more detail: a signature \Sigma of operation and
predicate symbols of finite arities freely generates an HD, which is
then factorized by the congruence generated by the axioms (in the
categorical jargon, the result would be called the classifying HD of
the theory). The "classifying" CA can be also generated in this way
but not freely because expressing finiteness of the arities needs
additional conditions that cannot be captures equationally (it is a
well-known fact that the class of locally finite CA of an infinite
dimension is not a variety, it is not a quasi-variety too). If we
consider signatures in which all symbols have the same countable arity
\omega, then the corresponding CA is freely generated by \Sigma (and
then factorized by the theory congruence). The main advantage of HDs
over locally finite CAs is that the finiteness of the arities is
captured equationally (the trade-off is that HDs are algebras over
graphs while CAs are algebras over sets).
Note that the dimension/set of variables is a parameter in the above.
An essentially different way of algebraizing logic is when variables
are generators while the signature is a parameter. Semantically it
means that a model is an evaluation of variables, another evaluation,
even in the same carrier set, is another model. This is how validity
of implications is defined. Theories in such logic are congruences (in
contrast to Birkhoff's fully invariant congruences, when we talk about
the equational logic), and we may call this way of algebraizing logic
"congruental" (the term introduced by Blok and Pigozzi in their
seminal work on algebraic logic).
If Sign denotes a category of signatures and Log is a category of
logics algebraically defined in a suitable way, then the HDs/CAs' way
of algebraizing logic can be presented as a binary functor Sign x
Set^op --> Log (signature elements are generators, the set of
variables is a parameter). In congruental logic, we have a dual
situation described by a functor Set x Sign^op --> Log (variables are
generators, the signature is a parameter).
Details can be found in my paper
http://www.cs.toronto.edu/~zdiskin/Pubs/WAAL-97.pdf
full of conjectures (deep insights are also possible :-).
Zinovy
On 5/28/07, Bill Lawvere <wlawvere@buffalo.edu> wrote:
>
>
> Hyperdoctrines (in many variants) were introduced as an algebraic
> aspect of "proof theory" and as such are definitely not equivalent
> to cylindric algebras (or polyadic algebras or even various categorical
> formulations of logic). They involve fibered categories whose fibers
> are cartesian closed (and with adjoints between the fibers etc.).
> The poset reflection of these fibers are Heyting algebras. This
> reflection process was intuited already by Curry and was later called
> "the Curry-Howard isomorphism" even though this is a serious misnomer
> because it is very far from being an isomorphism.
>
> (See my paper Adjoints in and among bi-categories, Logic & Algebra,
> Lecture Notes in Pure and Applied Mathematics. 180:181-189.
> Ed. A. Ursini, P Agliano, Marcel Dekker, Inc. Basel, 1996,
> as well as the author's commentary on my paper Adjointness in
> Foundations, as reprinted in TAC.
> Recent papers of Matias Menni further clarify these developments,
> which were partly inspired by work of Hans Laeuchli.)
>
> Conceptually, the problem of presentation of a theory in algebraic
> logic by means of primitive predicates and axioms can be viewed as
> taking place in two steps: first the presentation of a hyperdoctrine
> with non-trivial fibers, and then the further collapse by imposing
> the condition that projection maps act as inverse to diagonal maps
> (within each fiber). This process can be localized. The problematic
> existential quantifier which is the core problem of proof theory:
> ("there exists a proof of ....") is thus split into several parts
> to be studied separately.
>
> I hope the above helps to clarify the relationship between two
> levels of categorical algebra.
>
> Bill
>
>
> ************************************************************
> F. William Lawvere, Professor emeritus
> Mathematics Department, State University of New York
> 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
> Tel. 716-645-6284
> HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere
> ************************************************************
From rrosebru@mta.ca Thu May 31 07:48:21 2007 -0300
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Dear all,
This is to announce the availability of a preprint
"Infinitesimal cubical structure, and higher connections"
The preprint can be downloaded from
http://arxiv.org/abs/0705.4406
or from my home page
http://home.imf.au.dk/kock/
In the context of Synthetic Differential Geometry, we describe a
notion of higher connection with values in a cubical groupoid. We do
this by exploiting a certain structure of cubical complex derived
from the first neighbourhood of the diagonal of a manifold. This
cubical complex consists of infinitesimal parallelepipeda.
Yours
Anders
From rrosebru@mta.ca Sun Jun 3 21:50:19 2007 -0300
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From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
Subject: categories: Re: hyperdoctrines and cylindric algebras
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Couldn't one say that cylindric (and polyadic) algebras are awkward (from a
categorical point of view) formulations of posetal hyperdoctrines over
FinSet^op whose fibres are boolean algebras. So the pet objects of the
algebraic logicians are certain *presentations* of particular hyperdoctrines.
All this was worked out in a couple of papers by A. Daigneault beginning
of 70ies.
There is a lot of work by the algebraic logicians which I am not too familiar
with. There arises the question whether their work is of any use for questions
naturally arising to the categorical logician. That's how I understood Alex'
question and what I'd like to know myself.
Halmos was one of the first working on algebraic logic in the 50ies (polyadic
algebras) and was later positive w.r.t. categorical logic. That's what I have
heard of. Did he consider categorical logic as the "right formulation" of his
original aims? Maybe senior categorists do know about this?
Thomas